Hello sito: In reading your post I wasn't sure if you are asking if it's weird to feel anxious about spending the money on a new bike; or if you were asking it it's weird to try to alleviate anxiety by spending money (in this case, on a new bike.) Either way, though, no it's not weird at all.

If you want a new bike, & you can afford it, I'd say... go for it! Biking is great exercise.
Certainly almost everyone, I think, feels some anxiety when spending large amounts of money.

It's also not unusual at all for people who experience anxiety to try to lessen their anxiety by spending money.

I personally spend almost nothing at this point in my life. But, as I look back over the years, I wince at all of the money I spent trying to alleviate the depression, stress & anxiety I lived with day-in & day-out.